Renewable Resources Management : Two Proposed Dynamic Optimal Control Models

Dynamic modeling is general and recently the most interesting perspective to solve a dynamic economic problem based on Pontryagin’s maximum principle. Moreover, according to traditional economic theory, up to the middle of twentieth century, production functions are built without taking into account inputs’ scarcity. Nowadays however, it is clear that both inputs are depletable quantities and a lot of constraints are imposed in their usage in order to ensure economic sustainability. For example, the input “oil”, used in the production is a not renewable resource, can be exhausted. In a similar way, every biomass residing in ecosystems is a resource that can be used in a generalized production function for capital accumulation purposes but the latter resource is a renewable one. The contribution of this paper is the presentation of two renewable resources dynamic models in order to extract the optimal trajectories of the state and control variables for the optimal control economic problem. Authors attempt to show how methods of infinite horizon optimal control theory have been developed for renewable resources models